<title>Modal strain energy method critically revised</title>

When the vibration of a structure is considerably magnified by resonance effects, adding of damping is an effective method to reduce the level of vibration. Viscoelastic materials are generally used as an instrument to increase the amount of damping in the structure. The constrained-layer damping (CLD) method involves sandwiching a viscoelastic damping medium between two outer layers. The most important parameters which influence the dynamic behavior of a CLD system are the geometrical dimensions and the frequency dependent material properties of the viscoelastic material. Therefore, a direct solution of the equation of motion in the frequency domain seems to be the only valid solution technique. However, this method has to be rejected from a computational point of view when dealing with large structures. The mode superposition method is a powerful solution method to characterize the dynamic response of a large structure. The two basic assumptions to apply this method are that the material properties are constant and that the damping is proportional which is not the case for a CLD system. In the paper, four different solution techniques based on the solution of a (non- linear) eigenvalue problem are presented to predict the dynamic behavior of a simple supported sandwich layer system due to a uniform base excitation. The damping ratio of each eigenmode is calculated by the Modal Strain Energy method. Each proposed technique is validated in terms of accuracy and computational effort.